Frequency separator



E. A. J. MARCATILI FREQUENCY SEPARATOR April 24, 1962 Filed June 9, 1959 lNl/ENTUR EAJMARCAT/L/ ATTORMEV wSQ" United States This invention relates to electromagnetic wave transmission systems, and in particular to arrangements for separating a plurality of discrete channels or bands of frequencies propagating in a common transmission line.

It is frequently necessary, in high frequency multichannel transmission systems, to segregate the individual channels propagating within a common transmission path in order to amplify the wave energy or ultimately to use it. Because of this recurring necessity, it is desirable that the branching networks be capable of handling as broad a frequency range as possible, yet still be simple and efiicient in their operation. However, there are numerous practical considerations which limit the width of the spectrum that can be efliciently handled.

It is the broad object of this invention to extend the bandwidth over which elficient channel separation may be performed.

Consider a waveguide carrying a very broad spectrum of wave energy. The most obvious way to separate the bands within the spectrum is by simply cascading a series of channel-dropping filters. These filters generally consist of a through path and associated resonant elements tuned to the frequency to be dropped. In the conventional way, the channels are separated in order, either by starting from the high end of the spectrum or from the low proximately equal to 2. In a cylindrical waveguide, propend. However, if the lower channels are dropped first, in

a system using tuned cavities, for example, the ratio of the resonance frequencies of the first and second cavity modes will limit the frequency spectrum since the large cavities needed to resonate at the lower frequencies will also be capable of resonating at some higher frequencies defined by this ratio. This will either cause the higher frequencies to be rejected or, at the very least, will cause the generation of spurious modes and increase the losses in the system. If, on the other hand, it is attempted to drop the higher frequencies first, ,the cross section of the through guide, being a single mode guide, will be cut ofi for the lower part of the spectrum.

An alternate arrangement consists in splitting the spectrum into two or more smaller bands which are physically separated, and then dropping the channels in each subband in accordance with either of the conventional arrangements described above. However, this'alternate arrangement requires a number of bandpass filters capable of splitting the broad spectrum into two or more parts and is not, therefore, as attractive a method as the simple series arrangement described above.

It is, therefore, the specific object of this invention to separate, by means of a simple series arrangement of filters, the individual channels from within a broadband multichannel transmission path where the channels extend over a frequency range greater than an octave.

In accordance with the invention, a frequency spectrum extending over a range of frequencies f, to f, is divided into four subbands such that the end frequencies f,, and i and the intermediate frequencies f f and f defining the subbands, are related as follows:

fawn/twat,

and

agating the circular electric mode, n is. approximately equal to 1.83.

It should be noted, however, that the division con-- templated here is not a physical division as suggested in the alternate arrangement discussed above. Rather, it is merely an assigning of reference frequencies for determining the bandwidth and the order in which the various channels are separated from the common wave path.

The resonant cavities associated with the channel-dropping filters are proportioned so that the ratio between the resonant frequencies of the second and first cavity modes is n The order of dropping the subbands is then f to 2 from to f from f to f, and f to r By dividing the spectrum and dropping the subbands in accordance with the above plan, the maximum ratio of frequencies that can be separated by a simple series arrangement of channel-dropping filters is raised from n ton The technique described may be applied to any type of single mode Waveguide system.

These and other objects and advantages, the nature of the present invention, and its various features, will appear more fully upon consideration of the various illustrativeembodiments now to be described in detail in connection- FIG. 3 shows, by way of illustration, a portion of av channel-dropping filter using rectangular waveguides and comprises a through guide and a resonant cavity; and

FIG. 4 shows, by way of illustration, a portion of a, channel-dropping filter using cylindrical waveguides comprising the through guide and a resonant cavity.

Referring to FIG. 1, there is shown in block diagramform the channel separating arrangement in accordance with the invention. In this figure there is represented a wave path 10 carrying a plurality of infomnationbearing channels distributed over a very broad frequency spectrum. In particular, the channels are shown as extending from a frequency f, to a frequency i In accordance with the invention, the spectrum f,. to f is divided into four subbands, f, tof f to R, f to f and f to f.,. This division is made in accordance with requirements which will be explained in greater detail hereinafter. It should be noted that the particular frequencies f,, f ,f f -and f do not necessarily designate channel frequencies. Thus, for example, there is shown in FIG. 2, by way of illustration, a portion of the frequency spectrum containing twelve channels f f f propagating along a common transmission path and which are to be separated therefrom. In a system designated in accordance with the invention, the lowest frequency of channel f i.e., f,,, and the highest frequency of channel 12, i.e., f would be related by I b="1/sla fe 2/3fa fa= fa (4) These relationships are derived from the following requirements, namely that:

where n is a characteristic of the wave pathand is the ratio of the second mode cut-off frequency to the first mode and ' Patented Apr. 24, 1962 out-ofi frequency. For rectangular waveguide n is approximately equal to 2. In a cylindrical waveguide propagating the circular electric mode n is approximately equal to 1.83.

The intermediate frequencies f and f are also shown in'FlG. 2. It will be noted that these may, but need not, correspond to any of the channels f f They merely provide the groupings which allow for an orderly sequencefor separating purposes.

Referring again to FIG. 1, wave energy in path 19 is applied to a first set of channel-separating filters 11, Wherein the channels included within the subband between f and i are dropped. The filters indicated by block 11 comprise a suflicient number of cascaded filters of suitable design to separate those channels within the range f to f5. From PEG. 2, it is noted that there are three channels, f f and f within the designated range. These are dropped in any convenient order. As shown in FIG. 1, they are separated in descending order, i.e., the highest frequency channel, i is dropped first; channel f next and channel f last.

The channels in the remaining portions of the spectrum from f,, to f and from f to i are propagated through filter 11 and are applied to a second group of filters 12. The latter, as before, comprises a series of individual filters tuned to separate those channels within the designated subbandextending from f to f,,. This, from FIG. 2, is seen to include channels f f and f which we shown as being dropped in ascending order, i.e., the lowest frequehcy first. As'indicated above, the order of separation within any specific subband is a matter of convenience.

The remaining subbands, f to f and 7",, to f, are applied to the third group of filters 13 where channels f f j and f are separated. v This is followed by the separation of thechannels f and L; in subband f to f in the last 'g'rou-p of filters 14.

While the filte'r's'are shown as collected in four separate groh'ps'll, 12, 13, 14, this'is done only for the purposes of emphasis in the explanation of the operation of the invention. In practice, the individual filters are arranged in series, eachtuned to a preassigned channel, but in the sequential order indicated above.

The particular channel-separating filter used will "ary with the mode in which the energy is being propagated. For example, in systems propagating the circular electric mode of wave energy, the filter may be of the type disclosed in my copending application Serial No. 816,257, filed May 27, 1959, which utilizes mode conversion techniques to' achieve channel separation. Other types may be used, however, without in any way detracting from the effectiveness of the arrangement.

To understand the reasons for the particulardr'opping sequence used and the relationships among the frequencies f 'to f,,, it is necessary to understand specifically what deleterious conditions are sought to be avoided by the invention. This may best be understood by considering, for amohient; the transmission conditions in an actual network. For example, a'dropping filter generally comprises a through guide and a number of coupled resonant cavities associated'therewith which are tuned to the frequency of the channel to be dropped. To avoid moding, the through guide is generally proportioned to support only the first order mode of the channel to be dropped. However, since it is nece ssary that the guide be made as large as possible, the guide is proportioned to be just below cut-off for the second order mode at this frequency. If, for example, we consider the rectangular waveguide shown in FIG. 3 this means that the width, b, of the through guide 34 is equal to one wavelength of the frequency of the channel to be dropped. If the channels are dropped in descending order, the guide will be cut ofi for all frequencies below one half this frequency (the guide will be less than half a wavelength wide). Consequently, the maximum spectrum that'canbe' multiplexed in a system in which the 4. channels are separated in simple descending order, will have a bandwidth ratio of two to one.

If, on the other hand, the channels are sought to be dropped in ascending order, cut-off is not a problem since by making the guide wide enough for the lowest frequency it will, of necessity, be capable of passing the higher frequencies. However, here the problem is one of multiple resonances in the filter cavities which may prematurely drop or reject one of the higher frequenciesor, at the very least, cause losses in the system due to spurious moding' or undesirable resonances. This situation arises as a consequence of the fact that a cavity may resonate in many modes depending upon the exciting frequency. Thus, a cavity proportioned to resonate at the lowest frequency in the spectrum will also be capable of resonating at one of the higher frequencies. In fact, the next resonant mode for the rectangular cavity 31, of the type Shown in FIG. 3, will be no greater than about 1.78 times the dominant cavity mode frequency. Thus, to attempt to drop the lowest frequency channel first would put a limit on the spectrum that could be handled which is 1.78 times its lowest frequency. In accordance with the invention, both of the above-described limitations are considered and the channels dropped accordingly.

Taking into account both of the above discussed factors, it becomes clear that the system mut be arranged so that the first channel to be dropped has a frequency which will not allow spurious modes to be generated at the higher frequencies and for which the through guide will not be below cut-off at the lower frequencies. Rewriting Equations 1 through '4 with the value 2 substituted for n gives:

from which it is seen that the frequencies between i and f satisfy the requisite conditions. Consider, for example,-

the highest frequency, f The through guide at the f iiiter is a single mode waveguide proportioned to be just below cut-off for the second order transmission mode at frequency f the TE mode, the guide is made approximately one wavelength wide. From Equation 9 it is seen that for the lowest frequency f which is half f&, the waveguide is half a wavelength wide or just wide enough to support propagation at frequency f,,. Consequently, none of the intermediate channels between f,, and f are cut oif. From Equations 9 and 10 it is likewise seen that the highest frequency f is only 1.26 times i Since'this ratio is substantially less than the maximum cavity mode ratio for'rectangular cavities, which is 1.78, the resonant cavities of the f filter can readily be designed to prevent any of the higher frequencies between i and i from exciting the cavities and thereby producing spurious resonances.

For frequency f the lowest frequency in this subband, a similar situation exists. From Equation 8 it is evident that the through guide is not cut off for any of the lower frequencies between f and f It is also evident from Equations 8 and 10 that all of the higher frequencies between f and f are between 1.26 and 1.59 times f Since above, the maximum ratio obtainable in a rectangular waveguide system is 2.

While the ratio n is a characteristic of the transmission path, the ratio between the resonant frequencies of the In a rectangular wave path transmitting second and first cavity modes is a function of the cavity geometry and consequently may be designed to have any particular value up to and including the maximum theoretical value of 1.78. From the preceding discussion relating to the frequencies in the subband f to f it was seen that this ratio should not be less than 1.59. However, if the second group of channels to be dropped (those lying between and f is considered, it is seen that the cavity mode ratio over a large portion of this subband should not be greater than 1.59. If it is, frequencies between f and I will be capable of resonating with some of the lower frequency cavities in the range between i and f As a practical matter, a safe procedure is to design all the cavities to have a cavity mode ratio equal to 1.59. In particular, a ratio of 1.59 is obtainable in a rectangular cavity when the cavity has a length l equal to /2)\ and a width w equal to 1.06 /2)\, where 7\ is the free space wavelength of the frequency to be dropped. In general, however, the cavity should be designed so that the cavity mode ratio is equal to 71 Designating the general cavity mode as TE where x, y and 2 refer to the number of half-cycle variations in the electrical field intensity in the respective directions indicated by the reference axes shown in FIG. 3, the first cavity mode is designated TE and the second cavity mode TE With the cavity dimensions proportioned as indicated above, frequency i would just be capable of exciting a cavity tuned to frequency f In general, however, f defining the upper limit of the frequency spectrum under consideration, will not contain an appreciable amount of energy, and consequently is not a problem.

The second group of channels to be dropped are those between f,, and f By fixing the cavity mode ratio at 1.59 (or n in general), the higher frequency channels capable of producing spurious resonances are limited to those frequencies between f and i However, since the channels between i and f have already been removed, this possibility does not create any problem and the channels between and f can be safely dropped.

Next in order are the channels between f and i The through waveguides being just at cut-01f for the second order modes between f and f are cut off for frequencies smaller than f However, since the frequencies between f and f have previously been removed, frequencies below f need no longer be considered. Finally, the subband f to f can be dropped because those higher frequencies which would also excite the resonant cavities tuned to this range lie between f and f are no longer present.

It should be noted that if the dropping sequence shown here is not used, the maximum ratio of frequencies that a simple series arrangement of rectangular filters could multiplex is 2:1. However, in accordance with the invention this ratio is increased to over 2.52:1.

In a system utilizing the circular electric TE mode of wave propagation the same principles apply. However, the frequency ratios vary slightly. In FIG. 4 there is shown two cylindrical waveguides 40 and 41 of radius r, supportive of the TE circular electric mode, separated by a coupling gap 42. Surrounding the gap is the coaxial cavity 43 of radius r and length L, tuned to the frequency of the channel to be dropped. In such a system, n is approximately equal to 1.83. Substituting this value of n in Equations 1 through 4 the following is obtained:

521.22,, 11 EM 12 f aL83f 13) 3:52.24 14 The general cavity mode that can be supported in the coaxial cavity is designated T prz in accordance with the indicated rz polar coordinate reference system. The ratio, 21 between the resonant frequencies of the sec- 6 ond cavity mode, designated TE and the first cavity mode, designated TEm, is 1.5 and is obtained when the cavity is proportioned so that where A is the free space wavelength of the frequency to be dropped.

A circular electric multiplexing system operated in accordance with the invention will have an effective bandwidth factor of 2.24 as compared with 1.83 for a simple series channel-separating scheme.

In all cases it is understood that the above-described arrangements are illustrative of a small number of the many possible specific embodiments which can represent applications of the principles of the invention. Numerous and varied other arrangements can readily be devised in accordance with these principles of those skilled in the ant without departing from the spirit and scope of the invention.

What is claimed is:

1. In an electromagnetic wave transmission system, means for separating a plurality of channels in a frequency spectrum extending from a first frequency f,, to a last frequency i comprising a plurality of channeldropping filters sequentially arranged to separate the channels in the bands from f to 7 from f to ;f,,, from f to f and from f to f in the indicated order, where fb= fa. fc fa, fd= fw and fe= fm and Where n is a characteristic of the wave path and is the ratio of the second mode cut-off frequency to the first mode cutoff frequency.

2. The combination according to claim 1 wherein n is approximately equal to 2.

3. The combination according to claim 1 wherein n is approximately equal to 1.83.

4. In a broadband rectangular waveguide transmission system supportive of a plurality of spaced frequency bands of interest propagating in the TB mode of wave propagation extending from a first frequency to a second higher frequency f a plurality of filtering means each resonantly tuned to a given frequency of interest between said first and second frequencies and sequentially arranged to separate the bands in the frequency ranges from i to f from f to f from f to f and from f to f in the indicated order where am: i. it. 2

and where mans fa fb f0 5. The combination according to claim 4 wherein each of said filtering means comprises a right-angle parallelepiped cavity in whcih the length of said cavity is equal to V211 and the width w is equal to l.O6 /2 where A is the free space wavelength of the frequency of interest.

6. In a broadband cylindrical waveguide electromagnetic wave transmission system supportive of a plurality circular electric modeof wave propagation extending from 'afirst frequency f to -a second higher frequency f a plurality of filtering meanseach' resonantly tuned to a given frequency of interest between said first and said second frequency sequentially arranged to separate said bands in the frequency ranges from f to f r from f to f from f to f and from f to f,, in the indicated order Where f ELSOf 7. Themethod of separating abroad band of wave energy havingfrequencies extending from f -to a higher frequency f into a plu'rality'of channels each of smaller bandwidth than said band, comprising the steps of designating intermediate frequencies 15,, f and f within said band for which and f /f are both equal to the ratio 8 1 of the cut-0E frequency of the second order mode of propagation of the wave path supporting said energy to the cut-01f frequency'of the first'order mode therein and for'which f /f =f /f =f '/f separating these channels occurring between the" intermediate frequencies i and f subsequently separating those channels occurring be tween the frequencies f and f and then those occurring between i and fa and finally those occurring between ft: and b References (Iited in the file of this patent UNITED sTATEs'PATENTs 

